{"record":{"author":{"account_ref":null,"orcid":null},"builds_on":[],"content_schema":"pubphys.content.revision/1","content_sha256":"6971b074b20ab13479d53f6e5b9e25cd291f497b3db49b8e4542bd0309ad63a8","created":"2026-10-03T07:18:09Z","files":[],"origin":{"assisted_by":[],"kind":"seed"},"parents":["5475cf5dc5b1a72283d26dc95dc6e00d7ea4e00096a7c6492e409a1816eeb011"],"salt":"70b6fcc77e359d179fd9988f5c91779201169a2f8089f31fe9bfcb191111abf6","schema":"pubphys.record/2","site":"pubphys.com","target":null,"type":"revision"},"content":{"answer_type":"proof","assisted_by":[],"external_id":"qi.classical-simulability.t-state-stabilizer-rank","kind":"well-posed","literature_status":"open","n":"1","parents":[],"plain":"Circuits built from one special gate family can be simulated fast classically; adding extra 'magic' states makes them universal. The best classical simulators run in time set by a number called the stabilizer rank, and no one has proven that it must grow exponentially.","posed_since":"2016","precise":"The stabilizer rank $\\chi(\\psi)$ is the least number of stabilizer states whose linear combination equals $\\psi$. Prove chi(|T>^(tensor n)) >= 2^(c n) for some constant $c > 0$, where |T> = (|0> + e^(i pi/4) |1>)/sqrt(2). Known upper bounds are of order $2^{0.4 n}$ (approximate exponent) and known lower bounds are only polynomial in n.","problem_ref":null,"references":"","settled_by":"A proof of an exponential lower bound, or a construction with subexponential rank.","status_note":"","title":"Exponential lower bound on the stabilizer rank of magic states","topic_ref":"2c6beabcac690dc93131e1fe587b8b4a01c9e2df57eeabff1c22a4fbf820561b"},"attested":{"attestation":{"batch":null,"client_id":null,"id_token_sha256":null,"kind":"platform"},"record_hash":"d5c69c47dcdea08ce8133a347ee03bb57ac1f35aed63c34c474676c55f410806","schema":"pubphys.attested/1"},"envelope":{"attested_hash":"2e769dab3f8057f02cb910b4005aeda1cf1857689deb8f8bf54d712acdbe7217","platform_signature":{"key_id":"c6afc19b31429869751f06879c75cd64ea92654423d15b44be775bf1310a60da","sig":"9jVAsKhNuDd_ak-KxrnN-3Wolk16YvGe5MfLr2pqIaH_fi-RlP9L7AN0XePC4jXjRkWm0Sg6KXa7N7hNk6CKBQ"},"schema":"pubphys.envelope/1"},"record_hash":"d5c69c47dcdea08ce8133a347ee03bb57ac1f35aed63c34c474676c55f410806","leaf_index":1976}